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# Solving Linear Equations

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### Solving Linear Equations

1. 1. 1.3: Solving Linear Equations <ul><li>Goals: </li></ul><ul><li>Solve a linear equation for a specified variable </li></ul><ul><li>2. Describe the steps necessary to solving linear equations </li></ul>
2. 2. Review of Terms <ul><li>1) Variable </li></ul><ul><li>2) Coefficient </li></ul><ul><li>3) Constant </li></ul><ul><li>4) Expression </li></ul><ul><li>5) Equation </li></ul>Throughout Algebra 2, you will hear many different terms being used to describe the parts of an equation or expression. You will need to know the definition of the following terms throughout the course.
3. 3. Review of Terms <ul><li>1) Variable </li></ul><ul><li>2) Coefficient </li></ul><ul><li>3) Constant </li></ul><ul><li>4) Expression </li></ul><ul><li>5) Equation </li></ul>Variable: A letter which is used to represent an unknown number or value. Any letter can be used as a variable.
4. 4. Review of Terms <ul><li>1) Variable </li></ul><ul><li>2) Coefficient </li></ul><ul><li>3) Constant </li></ul><ul><li>4) Expression </li></ul><ul><li>5) Equation </li></ul>Coefficient: The number in front of a variable in a mathematical equation or expression. The coefficient is actually being multiplied by the variable Coefficient: 3 Means: 3 times x Coefficient: ¼ Means: ¼ times x 2
5. 5. Review of Terms <ul><li>1) Variable </li></ul><ul><li>2) Coefficient </li></ul><ul><li>3) Constant </li></ul><ul><li>4) Expression </li></ul><ul><li>5) Equation </li></ul>Constant: A number being added or subtracted from a variable in an equation or expression. The constant in the above expression is: 9
6. 6. Review of Terms <ul><li>1) Variable </li></ul><ul><li>2) Coefficient </li></ul><ul><li>3) Constant </li></ul><ul><li>4) Expression </li></ul><ul><li>5) Equation </li></ul>Expression: Contains at least one variable. <ul><ul><li>Examples: </li></ul></ul>
7. 7. Review of Terms <ul><li>1) Variable </li></ul><ul><li>2) Coefficient </li></ul><ul><li>3) Constant </li></ul><ul><li>4) Expression </li></ul><ul><li>5) Equation </li></ul>Equation: A sentence that states that two mathematical expressions are equal. <ul><ul><li>Examples: </li></ul></ul>
8. 8. Steps to Solving Linear Equations <ul><li>Simplify each side of the equation, if needed, by distributing or combining like terms. </li></ul><ul><li>2. Move variables to one side of the equation by using the opposite operation of addition or subtraction. </li></ul><ul><li>3. Isolate the variable by applying the opposite operation to each side. </li></ul><ul><ul><li>a. First , use the opposite operation of addition or subtraction. </li></ul></ul><ul><ul><li>b. Second , use the opposite operation of multiplication or division. </li></ul></ul><ul><li>4. Check your answer. </li></ul>
9. 9. Simplify: Use the distributive property <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
10. 10. Simplify: Combine like terms <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
11. 11. Isolate Variables: Undo the addition <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
12. 12. Isolate Variables: Undo the multiplication <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
13. 13. Check your answer: Substitute the value of x back in <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
14. 14. <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>The answer is true; therefore, the vale of x is true. EXAMPLE :
15. 15. Simplify: Use the distributive property <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
16. 16. Move Variables: Move the -15x to the other side of the equation. <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
17. 17. Isolate Variables: Undo the addition <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
18. 18. Isolate Variables: Undo the multiplication <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
19. 19. Check your answer: Substitute the value of x back in <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
20. 20. The answer is true; therefore, the vale of x is true. <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
21. 21. Isolate Variables: Undo the addition <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
22. 22. Isolate Variables: Undo the division <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
23. 23. Isolate Variables: Undo the multiplication <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
24. 24. Check your answer: Substitute the value of x back in <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
25. 25. The answer is true; therefore, the vale of x is true. <ul><li>STEPS TO SOLVING : </li></ul><ul><li>1) Simplify </li></ul><ul><li>2) Move Variables </li></ul><ul><li>3) Isolate Variables </li></ul><ul><li>a. Undo addition/subtraction </li></ul><ul><li>b. Undo multiplication/division </li></ul><ul><li>4) Check your answer </li></ul>EXAMPLE :
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